Use this if you are using igraph from R
Calculates the Google PageRank for the specified vertices.
page_rank(graph, algo = c("prpack", "arpack", "power"), vids = V(graph), directed = TRUE, damping = 0.85, personalized = NULL, weights = NULL, options = NULL) page_rank_old(graph, vids = V(graph), directed = TRUE, niter = 1000, eps = 0.001, damping = 0.85, old = FALSE)
graph 
The graph object. 
algo 
Character scalar, which implementation to use to carry out the
calculation. The default is 
vids 
The vertices of interest. 
directed 
Logical, if true directed paths will be considered for directed graphs. It is ignored for undirected graphs. 
damping 
The damping factor (‘d’ in the original paper). 
personalized 
Optional vector giving a probability distribution to calculate personalized PageRank. For personalized PageRank, the probability of jumping to a node when abandoning the random walk is not uniform, but it is given by this vector. The vector should contains an entry for each vertex and it will be rescaled to sum up to one. 
weights 
A numerical vector or 
options 
Either a named list, to override some ARPACK options. See

niter 
The maximum number of iterations to perform. 
eps 
The algorithm will consider the calculation as complete if the difference of PageRank values between iterations change less than this value for every node. 
old 
A logical scalar, whether the old style (pre igraph 0.5) normalization to use. See details below. 
For the explanation of the PageRank algorithm, see the following webpage: http://infolab.stanford.edu/~backrub/google.html, or the following reference:
Sergey Brin and Larry Page: The Anatomy of a LargeScale Hypertextual Web Search Engine. Proceedings of the 7th WorldWide Web Conference, Brisbane, Australia, April 1998.
igraph 0.5 (and later) contains two PageRank calculation implementations.
The page_rank
function uses ARPACK to perform the calculation, see
also arpack
.
The page_rank_old
function performs a simple power method, this is
the implementation that was available under the name page_rank
in pre
0.5 igraph versions. Note that page_rank_old
has an argument called
old
. If this argument is FALSE
(the default), then the proper
PageRank algorithm is used, i.e. (1d)/n is added to the weighted
PageRank of vertices to calculate the next iteration. If this argument is
TRUE
then (1d) is added, just like in the PageRank paper;
d is the damping factor, and n is the total number of vertices.
A further difference is that the old implementation does not renormalize the
page rank vector after each iteration. Note that the old=FALSE
method is not stable, is does not necessarily converge to a fixed point. It
should be avoided for new code, it is only included for compatibility with
old igraph versions.
Please note that the PageRank of a given vertex depends on the PageRank of all other vertices, so even if you want to calculate the PageRank for only some of the vertices, all of them must be calculated. Requesting the PageRank for only some of the vertices does not result in any performance increase at all.
Since the calculation is an iterative process, the algorithm is stopped after a given count of iterations or if the PageRank value differences between iterations are less than a predefined value.
For page_rank
a named list with entries:
vector 
A numeric vector with the PageRank scores. 
value 
The eigenvalue corresponding to the eigenvector with the page rank scores. It should be always exactly one. 
options 
Some information about the underlying
ARPACK calculation. See 
For page_rank_old
a numeric vector of Page Rank scores.
Tamas Nepusz ntamas@gmail.com and Gabor Csardi csardi.gabor@gmail.com
Sergey Brin and Larry Page: The Anatomy of a LargeScale Hypertextual Web Search Engine. Proceedings of the 7th WorldWide Web Conference, Brisbane, Australia, April 1998.
Other centrality scores: closeness
,
betweenness
, degree
g < sample_gnp(20, 5/20, directed=TRUE) page_rank(g)$vector g2 < make_star(10) page_rank(g2)$vector # Personalized PageRank g3 < make_ring(10) page_rank(g3)$vector reset < seq(vcount(g3)) page_rank(g3, personalized=reset)$vector